Finite Group Databasebeta

← C3×#70638 #11786813

Subgroups — C3×#70638 #11786813

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic
2C2×C32×#107C211yesmaximal, characteristic, complemented
3C2×C3×#821C211yesmaximal, characteristic
4C3×#4972C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic
6C3×#4550C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#1862—31nomaximal
9#70638C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C22×C3×C4×D3—21no—
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—21no—
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#893—22no—
21C3×#893—22no—
22C32×#107—22no—
23C3×C3⋊#95—21no—
24C3×#821C414yescomplemented
25C3×#809—22no—
26C2×C3×C4×D4—31no—
27C2×#893C2×C311yescharacteristic
28C2×C3×#107—21no—
29C2×C3×#107D311yescharacteristic, complemented
30C2×C3×#107C2×C311yescharacteristic, complemented
31C2×C3×#102—31no—
32C2×C3×#102—31no—
33C3×#389—31no—
34C2×#821C2×C311yescharacteristic
35#4972C2×C311yescharacteristic, complemented
36C2×#809C2×C311yescharacteristic
37C3×#340—31no—
38C3×#336—31no—
39#4550C2×C311yescharacteristic, complemented
40#4529C2×C311yescharacteristic, complemented
41C23×C3×D3—21no—
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3×Dic3—21no—
46C22×C3×Dic3D411yescharacteristic
47C22×C3×Dic3D411yescharacteristic
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12C2×C412yes—
52C2×C3×D12D412yes—
53C2×C3×D12Q812yes—
54C2×C3×C4×D3—24no—
55C2×C3×C4×D3—42no—
56C2×C3×C4×D3—42no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C2×C32×C8C2×C412yescomplemented
60C32×C4⋊C4—21no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4D412yes—
64C3×(C2×D3)⋊C4—24no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3C2×C412yescomplemented
67C3×Dic3⋊C4—42no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#1862—31noSylow
74C22×C3×D4—31no—
75C23×C3×C4—61no—
76C22×D12C22×C311yescharacteristic
77C22×C4×D3—21no—
78C22×C3×C8—21no—
79C22×C3×C8—31no—
80C22×C3×C8C2×D311yescharacteristic
81C22×C3×C8C22×C311yescharacteristic
82C3×C4×D4—62no—
83C3×C4×D4—62no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—61no—
88C2×C3×C4⋊C4C2×D311yescharacteristic
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C4⋊C4C22×C311yescharacteristic
91C2×C3×C4⋊C4C22×C311yescharacteristic
92C2×C3×C22⋊C4—61no—
93C2×C3×C42—31no—
94C2×(C2×D3)⋊C4—21no—
95C2×C4⋊Dic3C22×C311yescharacteristic
96C2×Dic3⋊C4—21no—
97C2×C4×Dic3C22×C311yescharacteristic
98C22×C3⋊C8C22×C311yescharacteristic
99#893—22no—
100#893—22no—
101C3×#107—24no—
102C3×#107—22no—
103C3×#107—22no—
104C3×#102—34no—
105C3×#102—62no—
106C3×#95—61no—
107C3⋊#95—21no—
108#821C3×C414yescomplemented
109#809—22no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—22no—
112C22×C3×D3—22no—
113C22×C3×D3—22no—
114C22×C3×D3—41no—
115C22×C3×D3—41no—
116C22×C3×D3—41no—
117C22×C3×D3—41no—
118C2×C32×C4—22no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×Q811yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3D812yes—
139C3×D12—22no—
140C3×D12—22no—
141C3×D12—22no—
142C3×D12C4⋊C414yescomplemented
143C3×C4×D3—48no—
144C32×C8—22no—
145C3×C3⋊C8—41no—
146C2×C4×D4—31no—
147C2×#107C3×D311yescharacteristic, complemented
148C2×#102—31no—
149C2×#102—31no—
150#389—31no—
151#340—31no—
152#336—31no—
153C24×C3—61no—
154C23×D3—21no—
155C2×C3×D4—32no—
156C2×C3×D4—32no—
157C2×C3×D4—32no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—41no—
169C22×C3×C4—41no—
170C22×C3×C4—64no—
171C22×C3×C4—61no—
172C22×C3×C4—122no—
173C22×C3×C4—122no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C23×C311yescharacteristic
176C22×Dic3—21no—
177C22×Dic3C3×D411yescharacteristic
178C22×Dic3C3×D411yescharacteristic
179C2×D12—21no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12C2×C3×C412yes—
183C2×D12C3×D412yes—
184C2×D12C3×Q812yes—
185C2×C4×D3—24no—
186C2×C4×D3—42no—
187C2×C4×D3—42no—
188C2×C3×C8—22no—
189C2×C3×C8—22no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—22no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C2×C3×C8—61no—
198C2×C3×C8C4×D312yescomplemented
199C2×C3×C8C2×C3×C412yescomplemented
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—41no—
210C3×C4⋊C4—41no—
211C3×C4⋊C4—61no—
212C3×C4⋊C4—122no—
213C3×C4⋊C4#6712yes—
214C3×C4⋊C4C3×D412yes—
215C3×C22⋊C4—64no—
216C3×C42—61no—
217C3×C42—61no—
218(C2×D3)⋊C4—24no—
219C4⋊Dic3—21no—
220C4⋊Dic3C2×C3×C412yescomplemented
221Dic3⋊C4—42no—
222C4×Dic3—21no—
223C4×Dic3—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C22×C32C4×D411yescharacteristic
228C22×C32#12011yescharacteristic
229C22×C32C22⋊Q811yescharacteristic
230C22×C32C2×D811yescharacteristic
231C22×C32#13511yescharacteristic
232C22×C32AGL(1,ℤ/8)11yescharacteristic
233C22×C32#13711yescharacteristic
234C2×C3×D3—24no—
235C2×C3×D3—42no—
236C2×C3×D3—42no—
237C2×C3×D3—42no—
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C32×C4—42no—
242C32×C4—81no—
243C32×C4C2×C4⋊C411yescharacteristic
244C32×C4C4×D411yescharacteristic
245C32×C4C22⋊Q811yescharacteristic
246C32×C4#12311yescharacteristic
247C3×Dic3—22no—
248C3×Dic3—42no—
249C3×Dic3—41no—
250C22×D4—31no—
251C23×C4—61no—
252C22×C8—31no—
253C22×C8C2×C3×D311yescharacteristic
254C4×D4—62no—
255C4×D4—62no—
256C2×C4⋊C4—31no—
257C2×C4⋊C4—61no—
258C2×C4⋊C4C2×C3×D311yescharacteristic
259C2×C4⋊C4C2×C3×D311yescharacteristic
260C2×C22⋊C4—61no—
261C2×C42—31no—
262#107—22no—
263#102—34no—
264#102—62no—
265#95—61no—
266C23×C3—21no—
267C23×C3—62no—
268C23×C3—62no—
269C23×C3—62no—
270C23×C3—121no—
271C23×C3—121no—
272C23×C3—121no—
273C23×C3—121no—
274C23×C3D3×D411yescharacteristic
275C23×C3C2×C3×D411yescharacteristic
276C22×D3—22no—
277C22×D3—22no—
278C22×D3—22no—
279C22×D3—41no—
280C22×D3—41no—
281C22×D3—41no—
282C22×D3—41no—
283C3×D4—34no—
284C3×D4—62no—
285C3×D4—62no—
286C3×D4—62no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—32no—
296C2×C3×C4—42no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—42no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—62no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—81no—
315C2×C3×C4—81no—
316C2×C3×C4—81no—
317C2×C3×C4—81no—
318C2×C3×C4—128no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4C2×C4×D311yescharacteristic
322C2×C3×C4#23511yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×Q811yescharacteristic
325C2×C3×C4#23911yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327C2×C3×C4C22×C3×C411yescharacteristic
328C2×C3×C4C2×C3×D411yescharacteristic
329C2×C3×C4C2×C3×D411yescharacteristic
330C2×C3×C4C2×C3×Q811yescharacteristic
331C2×C3×C4C3×#4111yescharacteristic
332C2×C3×C4C3×#4111yescharacteristic
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—22no—
336C2×Dic3—21no—
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3—41no—
340C2×Dic3—41no—
341C2×Dic3C3×D812yes—
342D12—22no—
343D12—22no—
344D12—22no—
345D12C3×C4⋊C414yescomplemented
346C4×D3—48no—
347C3×C8—24no—
348C3×C8—22no—
349C3×C8—22no—
350C3×C8—121no—
351C3⋊C8—41no—
352C2×C32#38511yescharacteristic
353C2×C32C4×D811yescharacteristic
354C2×C32#44011yescharacteristic
355C2×C32#44711yescharacteristic
356C2×C32#45211yescharacteristic
357C2×C32#47411yescharacteristic
358C2×C32#47811yescharacteristic
359C3×D3—44no—
360C24—61no—
361C2×D4—32no—
362C2×D4—32no—
363C2×D4—32no—
364C2×D4—61no—
365C2×D4—61no—
366C2×D4—61no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—31no—
370C22×C4—31no—
371C22×C4—64no—
372C22×C4—61no—
373C22×C4—122no—
374C22×C4—122no—
375C22×C4C22×C3×D311yescharacteristic
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—61no—
379C2×C8—61no—
380C2×C8—61no—
381C2×C8C3×C4×D312yescomplemented
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—32no—
386C4⋊C4—61no—
387C4⋊C4—122no—
388C4⋊C4C3×#6712yes—
389C22⋊C4—64no—
390C42—61no—
391C42—61no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—64no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3—122no—
404C22×C3—122no—
405C22×C3—122no—
406C22×C3#89311yescharacteristic
407C22×C3#89611yescharacteristic
408C22×C3D3×D811yescharacteristic
409C22×C3#91111yescharacteristic
410C22×C3#91811yescharacteristic
411C22×C3#91911yescharacteristic
412C22×C3#93711yescharacteristic
413C22×C3C3×C4×D411yescharacteristic
414C22×C3C3×#12011yescharacteristic
415C22×C3C3×C22⋊Q811yescharacteristic
416C22×C3C2×C3×D811yescharacteristic
417C22×C3C3×#13511yescharacteristic
418C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
419C22×C3C3×#13711yescharacteristic
420C2×D3—24no—
421C2×D3—42no—
422C2×D3—42no—
423C2×D3—42no—
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—42no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—62no—
434C3×C4—82no—
435C3×C4—82no—
436C3×C4—81no—
437C3×C4—81no—
438C3×C4—122no—
439C3×C4—121no—
440C3×C4D3×C4⋊C411yescharacteristic
441C3×C4#89411yescharacteristic
442C3×C4C4×#6711yescharacteristic
443C3×C4#94611yescharacteristic
444C3×C4C2×C3×C4⋊C411yescharacteristic
445C3×C4C3×C4×D411yescharacteristic
446C3×C4C3×C22⋊Q811yescharacteristic
447C3×C4C3×#12311yescharacteristic
448Dic3—22no—
449Dic3—42no—
450Dic3—41no—
451C32#186211yescharacteristic, complemented, Sylow
452C23—62no—
453C23—62no—
454C23—62no—
455C23—121no—
456C23—121no—
457C23—121no—
458C23—121no—
459C23C3×D3×D411yescharacteristic
460D4—34no—
461D4—62no—
462D4—62no—
463D4—62no—
464C2×C4—22no—
465C2×C4—32no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—62no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—61no—
477C2×C4—128no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4C2×C3×C4×D311yescharacteristic
481C2×C4C3×#23511yescharacteristic
482C2×C4C3×D3×D411yescharacteristic
483C2×C4C3×D3×Q811yescharacteristic
484C2×C4C3×#23911yescharacteristic
485C2×C4C2×C3×#6711yescharacteristic
486C8—22no—
487C8—121no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—124no—
496C2×C3#487211yescharacteristic
497C2×C3#488911yescharacteristic
498C2×C3#489011yescharacteristic
499C2×C3#489111yescharacteristic
500C2×C3#498911yescharacteristic
501C2×C3#515611yescharacteristic
502C2×C3#518711yescharacteristic
503C2×C3C3×#38511yescharacteristic
504C2×C3C3×C4×D811yescharacteristic
505C2×C3C3×#44011yescharacteristic
506C2×C3C3×#44711yescharacteristic
507C2×C3C3×#45211yescharacteristic
508C2×C3C3×#47411yescharacteristic
509C2×C3C3×#47811yescharacteristic
510D3—44no—
511C22—64no—
512C22—122no—
513C22—122no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22—122no—
518C22C3×#89311yescharacteristic
519C22C3×#89611yescharacteristic
520C22C3×D3×D811yescharacteristic
521C22C3×#91111yescharacteristic
522C22C3×#91811yescharacteristic
523C22C3×#91911yescharacteristic
524C22C3×#93711yescharacteristic
525C4—42no—
526C4—62no—
527C4—81no—
528C4—121no—
529C4—122no—
530C4C3×D3×C4⋊C411yescharacteristic
531C4C3×#89411yescharacteristic
532C4C3×C4×#6711yescharacteristic
533C4C3×#94611yescharacteristic
534C3—21no—
535C3#7063811yescharacteristic, direct product factor
536C3C3×#186211yescharacteristic, complemented
537C2—124no—
538C2C3×#487211yescharacteristic
539C2C3×#488911yescharacteristic
540C2C3×#489011yescharacteristic
541C2C3×#489111yescharacteristic
542C2C3×#498911yescharacteristic
543C2C3×#515611yescharacteristic
544C2C3×#518711yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#107C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#107D3
hypocenterC3C3×#1862
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#107

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C32×#107C2semidirect
4. C3×#4972C2semidirect
6. C3×#4550C2semidirect
7. C3×#4529C2semidirect
9. #70638C3direct (N × H)
24. C3×#821C4semidirect
29. C2×C3×#107D3semidirect
30. C2×C3×#107C2×C3semidirect
35. #4972C2×C3semidirect
39. #4550C2×C3semidirect
40. #4529C2×C3semidirect
59. C2×C32×C8C2×C4semidirect
66. C3×C4⋊Dic3C2×C4semidirect
108. #821C3×C4semidirect
142. C3×D12C4⋊C4semidirect
147. C2×#107C3×D3semidirect
198. C2×C3×C8C4×D3semidirect
199. C2×C3×C8C2×C3×C4semidirect
220. C4⋊Dic3C2×C3×C4semidirect
345. D12C3×C4⋊C4semidirect
381. C2×C8C3×C4×D3semidirect
451. C32#1862semidirect
535. C3#70638direct (N × H)
536. C3C3×#1862semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#8932
C2×C32×#1072
C2×C3×#8212
C3×#49722
C2×C3×#8092
C3×#45502
C3×#45292
C3×#18623
#706383